To determine the percentage of air that will come in or out of the room when the temperature is reduced from 27°C to 17°C, we need to consider the ideal gas law. The ideal gas law states that the product of pressure (P), volume (V), and temperature (T) of a gas is proportional to the number of moles (n) and the gas constant (R). Mathematically, it can be expressed as:
PV = nRT
Since the pressure is assumed to be constant, we can simplify the equation as:
V₁ / T₁ = V₂ / T₂
where V₁ and T₁ represent the initial volume and temperature, and V₂ and T₂ represent the final volume and temperature.
Let's plug in the known values into the equation:
V₁ = 300 m³ T₁ = 27°C = 27 + 273 = 300K (converted to Kelvin)
V₂ = 300 m³ (the volume remains the same) T₂ = 17°C = 17 + 273 = 290K (converted to Kelvin)
Now we can solve for the ratio of the initial and final volumes of air:
V₁ / T₁ = V₂ / T₂ 300 m³ / 300K = 300 m³ / 290K
The volumes cancel out, and we are left with:
1 / T₁ = 1 / T₂
Now, let's calculate the percentage change in temperature:
Percentage change = [(T₂ - T₁) / T₁] * 100 = [(290K - 300K) / 300K] * 100 = -3.33%
Therefore, when the temperature is reduced from 27°C to 17°C while keeping the volume and pressure constant, the percentage change in the amount of air in the room is approximately -3.33%. This means that around 3.33% of the air will leave the room.